Introduction to higher order categorical logic

Higher-Order Categorical Grammar

Introduction to Categories and Categorical Logic

Preface The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain numerous exercises, and hopefully will prove useful for self-study by those seeking a first introduction to the subject, with fairly minimal prerequisite...

Higher-order Logic Programming Higher-order Logic Programming Y Contents 1 Introduction 3 2 Motivating a Higher-order Extension to Horn Clauses 5 3 a Higher-order Logic 12

Introduction to Decidability of Higher-Order Matching

Higher-order unification is the problem given an equation t = u containing free variables is there a solution substitution θ such that tθ and uθ have the same normal form? The terms t and u are from the simply typed lambda calculus and the same normal form is with respect to βη-equivalence. Higher-order matching is the particular instance when the term u is closed; can t be pattern matched to u...

Executing Higher Order Logic

We report on the design of a prototyping component for the theorem prover Isabelle/HOL. Specifications consisting of datatypes, recursive functions and inductive definitions are compiled into a functional program. Functions and inductively defined relations can be mixed. Inductive definitions must be such that they can be executed in Prolog style but requiring only matching rather than unificat...